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1
Preheat your broiler.
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2
Toss the eggplant with the salt. Place in a colander over a bowl to catch any liquid run-off. Tumble occasionally. Let the eggplant sit for 10 minutes or so before using.
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3
Heat a large cast-iron or other heavy-bottomed skillet over medium-high heat. Add the olive oil and swirl.
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4
When the oil wrinkles into a semi-psychedelic haze, just before it reaches the smoke point, add the eggplant in a single layer. Let cook for 2 minutes before attempting to stir.
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5
Now grab a wooden spoon. Saute the eggplant for about 5 minutes or until well browned and tender, stirring occasionally. Add the yellow onion and the garlic. Stir.
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6
Lower the heat to medium-low. Add the sugar, sherry vinegar, and thyme. Fold to integrate, and cook over low heat for 10 minutes, until the mixture softens and becomes unified.
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7
Turn off the heat. Let the eggplant mixture rest for a few minutes--right there in the pan.
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8
Place the bread slices on a baking sheet and broil until slightly charred on both sides, 1 minute per side. Remove the bread. Put the walnuts on the baking sheet in a single layer.
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9
Broil the walnuts until the first sign of char appears on a single nut piece. Remove from the oven and fold into the eggplant mixture. Add the parsley to the eggplant mixture.
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10
To serve, spoon a generous amount of eggplant mixture on the bread slices. Sprinkle evenly with the pecorino Romano.
